2nd Dub Side of The Moon (Easy Star Allstars) they also did one of the Radiohead albums, but that just doesn't work as well.
A lot of Richard Cheese's covers are funny and/or good. His version of Radiohead Creep is great, and Nivarna's Rape Me is something different in the chilled lounge/piano jazz style!

Another vote for Richard Cheese here. His version of "Baby got back" is truly top drawer.

On a slightly different note, check out the Balanescu Quartet's (they did the theme tune to University Challenge) versions of The Model, We are the Robots and a couple of other Kraftwerk tunes. They're ace!

Hard and Phirm's rodeohead medley? Yotube Link. Used to love than in years gone by, probably doesn't fit your requisite of a serious cover as although excellently done tongue's firmly in cheek. Got an album a while ago called Cosmosonica when I was going through a cover appreciation phase. NOt great tbh but loved the scissor sister's cover of Franz Ferdinand's 'take me out'.